The average selling price of a cup of coffee is $1.35 and the average variable expense per cup is $0.41. The average fixed expense per month is $1,600. How many cups of coffee would have to be sold to attain target profits of $3,700 per month?
(1.35 - 0.41)x = 1600 + 3700
n * 1.35 = 1600 + .41 n + 3700
.94 n = 5300
To determine the number of cups of coffee that need to be sold to attain a target profit, we need to consider the profit per cup of coffee.
Profit per cup of coffee = Selling price per cup - Variable expenses per cup
Given:
Selling price per cup = $1.35
Variable expenses per cup = $0.41
Profit per cup of coffee = $1.35 - $0.41 = $0.94
Now, we can calculate the number of cups of coffee that would have to be sold to attain the target profit:
Target profit per month = $3,700
Total fixed expenses per month = $1,600
Let the number of cups of coffee to be sold = X
Total profit = Profit per cup of coffee * Number of cups of coffee
Total profit = $0.94 * X
We know that:
Total profit = (Total revenue - Total expenses)
Total revenue = Selling price per cup * Number of cups of coffee
Total expenses = Variable expenses per cup * Number of cups of coffee + Fixed expenses per month
So, we have:
$0.94 * X = (Selling price per cup * X) - (Variable expenses per cup * X + Fixed expenses per month)
Substituting the given values:
$0.94 * X = ($1.35 * X) - ($0.41 * X + $1,600)
Now, we can solve this equation to find the value of X, which represents the number of cups of coffee that need to be sold:
$0.94X = $1.35X - $0.41X - $1,600
$0.94X = $0.94X - $1,600
$0.94X - $0.94X = - $1,600
0 = - $1,600
Since the equation has no solution, it implies that the target profit of $3,700 per month cannot be attained based on the given information.